effectiveness of mountaineering manual belay/abseil devices
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ORIGINAL ARTICLE
Effectiveness of mountaineering manual belay/abseil devices
W. J. Stronge • Mathonwy Thomas
� International Sports Engineering Association 2013
Abstract Mountaineers and rock climbers use a belay
device to increase tension in the rope that links the belayer
to a falling climber—this rope slows and finally stops the
fall. With a manual (passive) belay device the belayer can
hold a force of several kN although he/she applies a hand
force of only 0.2–0.35 kN on the rope; i.e. the device
increases the hand force by a factor between 5 and 10. This
investigation provides dynamic measurements of force
amplification by various manual belay devices when used
on a range of both wet and dry climbing ropes and it
examines the source of force amplification in these devices.
The force amplification is found to be due to a combination
of friction and distortion of the rope as it traverses around
tight corners within the device. In modern devices, the
tension amplification due to distortion exceeds that due to
friction.
Keywords Belay device � Friction � Amplification
factor � Device comparison � Climbing ropes
1 Introduction
The mountaineering term ‘‘abseil’’ or ‘‘rappel’’ describes a
controlled slide down a rope that is fixed to an anchor at the
top, while ‘‘belay’’ describes a procedure for limiting the
length of fall for a roped climber by either preventing or
controlling the slippage of the rope as it passes through the
belay. In both cases, the belayer/abseiler controls the rate at
which rope passes through the belay/abseil station by
tightening or loosening his/her grip on the ‘‘tail’’ end of the
rope. Since hand strength is normally insufficient to control
rope tensions that can be several times larger than body
weight, a belay/abseil device is typically used as a ‘‘force
multiplier’’ to increase the effective control hand force that
resists flow of the rope through the belay device [1–3]. To
carry less weight, most climbers carry a single device for
both abseiling and belaying.
Manual (passive) belay/abseil devices are designed
such that as the rope extends under a suddenly applied
load, it is required to follow a tortuous route slipping
around small radius corners in the device. As rope passes
through the device, friction between the aluminium
device and the polyamide rope dissipates energy. This
friction amplifies the hand force that restrains slippage of
rope through the device. The first devices were manu-
factured in the 1960s; they were thick aluminium plates
containing a pair of chamfered slots through which a
bight (loop) of rope could be passed (the Sticht plate).
On the back side of the plate, a carabiner was passed
through the loop and this carabiner was attached to the
belayer’s harness. The ‘‘live’’ end of the rope is con-
nected to the lead climber while the ‘‘tail’’ end is grip-
ped by the hand of the belayer. If the lead climber falls,
tension in the rope above the device can be as much as
10 times larger than the weight of the falling climber. To
arrest the fall, this tension must be resisted by the
product of the belayer’s grip on the tail of rope and the
amplification factor of the belay device [4].
The design of belay/abseil devices has undergone
minor changes from that of the original Sticht plate—the
radii of curvature around edges in the device have grown
tighter and V-grooved exit passages have increased
friction by increasing the normal force acting on the
rope. These changes have roughly doubled the
W. J. Stronge (&) � M. Thomas
University of Cambridge, Cambridge, UK
e-mail: wjs@eng.cam.ac.uk
Sports Eng
DOI 10.1007/s12283-013-0147-6
amplification of current manual belay devices in com-
parison with the Sticht plate.
Generally, it is believed that manual belay/abseil devi-
ces rely on friction to generate the multiplication in tensile
force in the rope between the ‘‘tail end’’ and the loaded
‘‘live end’’ of the device; i.e. the tensile load required to
induce slippage of the rope through the device is the sum of
friction in the device plus the grip force on the tail of the
rope [5]. If this conjecture is correct and Coulomb’s
coefficient of friction (COF) l is independent of normal
force, then across a device without grooves, the ratio
between the tensile load T1 on the live end and the grip
force T0 on the tail end of the device can be calculated as
T1=T0 ¼ elh;
where h is the sum of the angles through which the rope is
bent within the device. This expression, termed the capstan
or Euler equation, applies to sliding friction between a thin
flexible rope and a cylindrical drum. It describes a tension
ratio that is independent of the radius of curvature around
corners within the device. Minor effects due to elongation
of the rope and a power-law decreasing COF have been
considered by Jung et al. [6]. One question addressed in
this paper is whether surface friction between rope and
device is the only force that resists the rope being drawn
through a belay/abseil device.
2 Devices and ropes that were tested
2.1 Mountaineering/rock climbing ropes
Climbing ropes are required to be strong, elastic, light-
weight, easy to securely knot and have good resistance to
cutting over an edge. They not only hold a fallen climber,
but also bring the falling climber to rest without too large
an acceleration. Thus, they are elastic for tensile forces
somewhat larger than body weight but can suffer perma-
nent damage when required to hold a high load (a leader
fall with a Fall Factor [1.4) [5].
Currently, mountaineering or rock climbing ropes use
kernmantle construction; this has a central core composed
of a bundle of 9–11 cords—each with a large angle of
twist. The direction of twist for half the cords is clockwise
and the other half anti-clockwise so that under tension,
there is no net twist of the core. This core is contained
within a woven sheath which provides protection against
abrasion, dirt, uv-damage, etc. Dynamic climbing ropes are
made of Polyamide 6/6, a type of nylon.
Ropes for use in wet conditions can be purchased with
either the sheath or both core and sheath composed of fil-
aments that have been chemically treated to reduce water
absorption. Those with a treated sheath are termed ‘‘dry’’
while treatment of both sheath and core results in a ‘‘super
dry’’ or ‘‘golden dry’’ rope. The water repellent treatment
of the sheath of both dry and super dry ropes is thought to
increase their abrasion resistance and decrease friction
when running over rock or through an aluminium belay
device.
2.2 Belay/abseil devices for mountaineering ropes
Belay/abseil devices are used as a force multiplier so that
the grip force of one hand can control rope tension–tension
which can be several times larger than body weight.
Manual belay/abseil devices are required to be secure, easy
to set-up and lightweight; preferably, they are free of any
moving parts and difficult to assemble incorrectly. At least
two distinct types of devices are commonly used to assist a
belayer in holding a fall. Both types are typically made
of Aluminium which is lightweight and a good heat
conductor.
Huit Figure 8 or 8-Ring As the name implies, these
devices are shaped like the numeral 8 with a large and a
small hole. A bight (loop) of rope is passed through the
large hole and looped back around the neck that joins the
holes, before a carabiner (snap-link) is used to attach
the small hole to the belayer’s harness or the belay station
(see Fig. 1). In Fig. 1, the loaded rope enters the photo from
the top while the belayer grips the lower, tail of the rope.
Huit 8-Rings can be used with a wide range of different
diameter ropes. They are easy to set-up and operate
Fig. 1 Huit 8-Ring threaded with rope. Hand force applied to tail of
rope on right of device while the belayer is clipped to the ring at the
bottom
W. J. Stronge, M. Thomas
smoothly when abseiling/rappelling but in many cases,
they produce insufficient force for application as a belay
device. The device also tends to cause residual twist in the
rope which then untwists during subsequent abseils. The
8-Ring is larger and heavier than conical devices.
Tubular devices A wide range of plate or cone devices
have a pair of slots in the bottom of a truncated cone (see
Fig. 2a–c). They are known by trade names such as Sticht
plate, Black Diamond ATC, Petzl Verso and Petzl Reverso.
These devices are set-up by passing a bight of rope through a
slot and then clipping the bight of rope with a carabiner
which is attached to either the belayer’s harness or the belay
anchor. In almost all cases, a 2nd slot is provided for a second
rope which is commonly used either while abseiling or when
leading while using double rope technique.
Tubular devices or cones are small, lightweight and
simple to use for climbing ropes from 8.1 to 10.4 mm
diameter. The devices with V-shaped grooves in the exit
slot (Verso and Reverso) tend to be more effective than
devices without exit grooves. The action of the grooves is
similar to that of a V-belt pulley, essentially increasing the
normal force acting on the rope that is passing through the
grooved section of the device [7].
3 Measuring effectiveness of belay/abseil devices
The effectiveness of a belay device in amplifying the hand
force acting on the rope is obtained from a load amplifi-
cation factor;
Amplification ¼ T1=T0; ð1Þ
where T1 is the rope tension on the live side and T0 is the
rope tension on the tail side of the device. This amplifi-
cation also has been termed a brake factor [2, 9]. The load
amplification is obtained from measurements of the force
required to draw the rope through the device when the tail
end of the rope is loaded by a specified weight (i.e. the
hand force). Measurements of the load amplification factor
were made with the block and tackle rig illustrated in
Fig. 3 which was mounted on a tensile test machine. At the
device, the tension T1 was obtained from the recorded
tensile force at the load sensor, while the hand force
T0 = Mg was the weight Mg of a mass hung on the tail of
the rope. The purpose of the pulley system is to increase
the speed at which the rope could be drawn through the
device; the present tests were performed with a rope speed
through the device of 0.075 m/s and hand force angle
a = p/9.1
The tension required to draw the rope through the device
was measured for hand forces varying from 50 to 207 N.
These hand forces compare with a range of 150–350 N
measured for recreational rock climbers (see ‘‘Appendix
2’’). Figure 4 shows a set of typical traces obtained for
Fig. 2 Tubular belay devices a Sticht plate, b ATC, c Verso. Hand force applied to tail of rope on left of device while the round bar is a
carabiner attached to the belayer
1 Rope speed through the device had little effect on the amplification.
For each device, an increase in rope speeds from 0.042 to 0.074 m/s
resulted in less than 3 % decrease in amplification. This is in
agreement with experiments by Fenz [8] on friction between woven
PTFE and stainless steel but it contradicts the viscous force
assumptions made in the analysis of Fuss and Niegl [9].
Effectiveness of mountaineering manual belay/abseil devices
Fig. 3 Block and tackle rig used to increase rope speed through device. Notice that the hand force T0 acts on the rope which passes freely
through a hole in the lower test bar
Fig. 4 Regions 1–4 of tensile force at load sensor for hand forces of 9, 58, 107 and 156 N. Three tests at each hand force demonstrate
repeatability of measurement
W. J. Stronge, M. Thomas
hand forces of 9, 58, 107 and 156 N. This graph of force as
a function of time has an initial period (1) where the force
is being distributed through the various segments of rope,
period (2) where the rope is stretching, period (3) where
there is steady pulling of the rope through the device and
period (4) after the displacement of the cross-head on the
testing machine is stopped. The plateau region 3 of these
curves was taken as the steady state force required to pull
the rope through this system. The rope tension force T1 was
obtained from the measured force by a calibration which
took into account the measured friction in the pulleys as
well as the multiple strands of rope between the upper and
lower blocks.
3.1 Amplification factor of abseil/belay devices
For six new ropes with diameters ranging from 8.1 to
11 mm, Fig. 5 shows a comparison of the amplification
factor as a function of hand force for the Huit 8-Ring and
four different conical devices. For all ropes and devices,
Fig. 5 Amplification factor for various belay devices on 6 ropes; a 11 mm dia., b 9.7 mm dia.—Classic, no water repellent treatment, c 9.7 mm
dia.—Dry, d 9.7 mm dia.—Super Dry, e 8.1 mm dia.—Dry
Effectiveness of mountaineering manual belay/abseil devices
the amplification decreases with increasing hand force. It
will be shown that this is because of decreasing friction
with increasing hand force—a result that is contrary to
Coulomb’s law of friction where the COF l is independent
of the normal force.
Comparison of Fig. 5a–f shows that for all devices, the
amplification decreases with rope size; i.e. for the hand force
of any particular belayer T0, the rope tension T1 generated on
the ‘‘live’’ side of the device for an 11 mm diameter Apollo
rope is 70 % larger than that generated by at 8.1 mm dia. Ice
Line rope. For all rope diameters, the Reverso has the largest
amplification while the Huit 8-Ring and Sticht plate have the
smallest amplification. For large diameter ropes, the Sticht
plate is more effective than the 8-Ring while for small
diameter ropes, this order is reversed; otherwise, the ampli-
fication factor of different devices is in the same order,
independent of rope diameter or hand force. The effect of
rope diameter on amplification factor is shown directly in
Fig. 6 where for 3 different devices and ropes with diameters
that range from 8.1 to 11 mm, the amplification factor is
plotted as a function of hand force.
In every case, the largest amplification occurred with the
Reverso device and the smallest amplification occurred with
either the Sticht plate or the Huit 8-Ring. The amplification
of the Reverso benefits from thin walls which force the rope
to pass around small radius of curvature corners and a
V-grooved exit channel which effectively increases the
normal force acting within the device. Among the devices
being tested, the Sticht plate and Huit 8-Ring force the rope
to have a relatively large minimum radius of curvature—a
minimum radius of curvature that is more than twice as large
as that in the conical devices. Previous measurements of
amplification (braking coefficient) obtained during drop
tests using various devices with a 9.7 mm Booster rope gave
somewhat smaller amplification than the results of the
present investigation; nevertheless, these results were con-
sistent with the present measurements in that the smallest
amplification occurred with the 8-Ring [2].
For the Booster 9.7 mm diam. rope, the effect of water
repellent treatment on the amplification factor was mea-
sured. Both Dry and Golden Dry versions of this rope were
compared with the untreated Booster Classic. There was no
significant difference in the amplification factor for new
ropes in a dry state as a function of whether or not they had
received the water repellent treatment. For conical devices,
the untreated rope had a slightly larger amplification
whereas for the 8-Ring, the Booster Golden Dry rope had
the largest amplification, but these differences were small.
Fig. 6 Effect of rope diameter on amplification factor for a Reverso, b ATC and c Huit 8-Ring
W. J. Stronge, M. Thomas
3.2 Comparing amplification factor of used and new
ropes
Figure 7 shows the amplification factors as a function of
hand force for three different ropes which had experienced
usage as described in Table 1. These curves can be com-
pared with similar curves for new ropes (Fig. 7). The only
obvious signs of wear on these well-used ropes were some
broken threads protruding from the mantel and slight
darkening of the mantel colour. Despite wear being minor
in terms of the surface appearance, the amplification fac-
tors for used ropes were 10–20 % larger than those for new
ropes. Subsequently, we will show that the COF for these
used ropes also was larger than the COF for new ropes.
3.3 Comparing amplification factor of dry and wet
ropes
Figure 8 shows the amplification factors for the various
belay/abseil devices as a function of hand force for wet
and dry states of the untreated Booster Classic and the
water repellent Booster Golden Dry ropes. The wet state
was obtained by immersing the rope in water for 12 h
immediately prior to testing. Absorbed water acts as a
plasticizer that reduces the elastic modulus of yarn and
reduces the number of falls to failure; this occurs because
absorbed water molecules decrease the strength of
molecular hydrogen bonds within the polyamide fibres
[10, 11]. At the same time, water within the rope
Fig. 7 Amplification factor of devices on used ropes; a 10.2 mm dia. new, b 10.2 mm dia. used (1), c 10.2 mm dia. used (2), d 8.1 mm dia. new,
e 8.1 mm dia. used
Effectiveness of mountaineering manual belay/abseil devices
increases inter-yarn abrasion and causes some damage to
filament surfaces [12, 13].
As noted previously, in the dry state the Reverso device
on the untreated rope had a somewhat larger amplification
than the same device on the water repellent rope. For dry
rope, all other devices gave roughly the same amplification
for the treated and the untreated ropes.
The effect of water on the untreated rope was to
decrease the amplification factor for almost all devices on
the order of 15 %; i.e. the devices were less effective if the
rope was wet. The Huit 8-Ring was the only exception; on
the untreated rope, it showed a small increase in amplifi-
cation when the rope was wet rather than dry. For the water
repellent rope however, there was little difference in
effectiveness between dry and wet ropes. This decrease in
amplification was measured despite the COF of wet rope
being somewhat larger than that for dry rope (see
‘‘Appendix 2’’). In fact, both the Verso and Huit 8-Ring
devices were slightly more effective on wet rather than dry
rope. For both wet and dry ropes, the Verso and Reverso
provided the largest amplification while the Huit 8-Ring
and Sticht plate gave the smallest amplification.
4 Causes of the amplification factor
There seem to be two sources of retarding force acting in
belay/abseil devices, (a) friction of the tensioned rope
Table 1 Mountaineering rope characteristics
Rope
name
Diameter
(mm)
Treatment Notes
Apollo II 11 Dry Heaviest rope on test
Edlinger 10.2 Untreated New rope
Edlinger
(Used 1) 10.2 Untreated Used 35 days lead
rope ? 3 months top rope at
indoor wall
(Used 2) Used for 6 months as ‘in situ’
rope at indoor wall
Booster
Classic
9.7 Untreated New rope
Booster
Dry
9.7 Dry New rope
Booster
Golden
Dry
9.7 Super Dry New rope
Stinger
(used)
9.4 Dry 100 day’s use, both as a winter
and alpine rope. Later used
for 5 years to practice knots
Ice Line 8.1 Dry New rope
The Ice Line is designed for
use as a ‘half rope’; this rope
is at the lower limit of the
recommended range of rope
diameters for belay devices
Ice Line
(used)
8.1 Dry 9 seasons use for alpine, winter
and traditional rock climbing
Fig. 8 a Booster Classic (untreated) rope in both wet and dry states with each belay device, b booster Golden Dry rope in both wet and dry states
with each belay device
W. J. Stronge, M. Thomas
around corners and (b) inter-cord slippage due to bending
of the fibrous rope within the device.
(a) As the rope slides through the rounded corners in a
belay/abseil device, friction resists sliding of the rope. The
sliding friction is represented by the capstan equation for
slender ropes;
T1=T0 ¼ elh; ð2Þ
where h is the sum of the angles through which the rope is
bent within the device. The COF l in this equation is a
property of both the sheath of the rope and the Aluminium
surface over which it slides. This equation assumes sliding
throughout the entire contact area between the rope and a
cylindrical surface. It is noteworthy that the capstan
equation is independent of the radius of curvature of the
rope around the cylindrical surface—it is applicable also if
the radius of curvature is not constant. This source of
amplification, including the effect of the V-grooved exit
slots, has been described by Belofsky [7].
Measurements of the COF l shown in the Appendix,
Table 2, were made with the rope draped over a large
radius Aluminium cylinder; the ratio of cylinder radius Rcyl
to radius of a standard oval carabiner Rcrab was on the order
of Rcyl/Rcrab = 16. The aim of this large cylinder radius is
to make negligible any effect of bending on the amplifi-
cation factor.
In addition to measurements of the COF for dry ropes
shown in Table 2, similar measurements were made on
ropes that had been soaked in water for 12 h, Table 3. A
summary comparing the COF for wet and dry ropes, as
well as for new and used ropes is shown in Fig. 9. The
worn surface of used rope results in a small increase in the
COF; the wet rope resulted in a larger increase on the order
of 10–20 %. Notice that the rope used to obtain Fig. 9 was
an Edlinger with no water repellent treatment. However, a
similar increase in COF was obtained after the dry treated
Ice Line rope was soaked in water.
It is important to recognise that Fig. 9 indicates that for
both dry and wet ropes, the COF is decreasing with
increasing rope tension. This decrease contributes to the
decrease in amplification which occurs with increasing
hand force.
(b) But friction does not account wholly for the ampli-
fication of rope tension in a belay/abseil device. As shown
in Fig. 10, the amplification increases with decreasing
radius of edges in the device; i.e. with edge sharpness.
These measurements were made with the rope draped over
cylindrical bars so that h = p. For an edge radius similar in
size to the cross-sectional radius of a lightweight carabiner
(4.25 mm), friction can account for only 55 % of the
amplification. Conical belay devices incorporate even
smaller edge radii (on the order of 1.5–2 mm) that result in
a smaller part of the total amplification being due to fric-
tion. In Fig. 10, the best fit line for the effect of edge radius
on amplification is represented by
T1
T0
¼ 1:7þ 0:8Rrope
Redge
: ð3Þ
This amplification factor was obtained for large hand
forces, between 0.254 and 0.354 kN. In this range, the rope
tension caused by hand force has only an insignificant
effect on the dissipation due to bending.
Titt [1] has suggested that the additional, non-frictional
energy dissipation is related to bending the rope through
tight radius bends. Distortion of the cross-section results
from slippage between cords in the core of the rope
because of the difference in fibre length between the inside
0.0 0.2 0.4 0.60.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30co
effic
ient
of f
rictio
n, µ
hand force (kN)
New Dry EdlingerUsed (2) Dry EdlingerNew Wet EdlingerUsed (2) Wet Edlinger
Fig. 9 Comparison of friction coefficients for wet and dry, new and
used ropes (10.2 mm dia. Edlinger)
0.0 0.5 1.0 1.5 2.0 2.5 3.01.5
2.0
2.5
3.0
3.5
4.0
4.5 Ice Line 8.1mm 0.254kN Edlinger 10.2mm 0.254kNApollo 11mm 0.254kNIce Line 8.1mm 0.354kNEdlinger 10.2mm 0.354kNApollo 11mm 0.354kN
ampl
ifica
tion,
T1/
T0
edge sharpness, Rrope/Redge
Fig. 10 Amplification variation with edge sharpness ratio for hand
forces of 0.254 and 0.354 kN on new Ice Line, Edlinger and Apollo
ropes
Effectiveness of mountaineering manual belay/abseil devices
and the outside fibres in the core as it passes around a bend.
Part of this difference in length comes from a difference in
stretch of the fibres and the associated variation in fibre
tension across the core, but this difference also results in
shear stress and slip between the cords in the core. After a
tensioned rope has passed around a tight bend, it is
noticeable that the cross-section has changed from circular
to oval as a result of internal slippage between the cords,
although after a distance of perhaps five rope diameters
beyond the bend, the cross-section of the tensioned rope
has returned to circular.
Assuming that the result in Fig. 10 for negligible edge
sharpness represents solely the effect of friction between
the mantel and a smooth Aluminium device, and that the
effects of bending and friction are independent, an estimate
for amplification due both to mantel friction and rope
bending can be obtained as
T1
T0
¼ 1þ 0:47Rrope
Redge
� �elh: ð4Þ
While the experiments in Fig. 10 were performed with a
wrap angle of h = p, experiments by Titt [1] have shown
that for small wrap angles h\p/2 the tensile force
required to distort the cross-section of the rope increases
with increasing h. Titt estimated that for a 10 mm diameter
rope running through a Sticht plate with 4 mm radius bends
of 80�, 185� and 42�, that 61 % of the amplification factor
is from bending while the remaining 39 % is from friction.
Equation (4), which does not take into account any
variation of amplification due to bending with angle h,
provides an estimate that 38 % of the Sticht plate
amplification is due to bending and 62 % is from friction.
5 Conclusion
The amplification factor is a measure of effectiveness of
belay/abseil devices. Rope tension on the ‘‘live’’ side of the
device leading to the falling climber is the product of the
hand grip force on the rope and the amplification factor.
Amplification depends on both (1) friction between the
belay device and the nylon rope and (2) dissipation of
energy within the rope due to slip of cords and fibres as the
tensioned rope slides around small radius corners. In the
range of hand force 100–200 N, all ropes and devices show
a decrease in amplification with increasing hand force as
noted previously by Fuss et al. [8]; nevertheless, tension T1
in the ‘‘live’’ end of the rope continually increases with
increasing hand force. The decrease in amplification has
been related to the coefficient of sliding friction between
the mantel of the nylon rope and the aluminium device—a
friction coefficient which decreases with increasing normal
pressure (see ‘‘Appendix 1’’).
Tubular belay devices with ‘V-shaped’ exit grooves and
small radius edges provide amplification on the order of
50 % larger than that of the Huit 8-Ring or Sticht plate. For
a moderate hand force of 200 N on a dry 10.2 mm
climbing rope, the tubular devices (Verso, Reverso) have
amplification *8 while the Sticht plate and 8-Ring have
amplification *5. The ATC has a little larger amplification
than the Sticht plate or 8-Ring. Transverse V-shaped
grooves in the exit channel are the probable reason for the
superior performance of the Verso and Reverso; these
grooves increase the normal force in this segment of the
belay device. All belay devices have larger amplification
with larger diameter ropes and they are more effective with
worn rather than new ropes. For dry treated ropes in a dry
state, water repellent treatment has a negligibly small effect
on both the COF and the amplification factor.
After soaking in water for 12 h, climbing ropes without
water repellent treatment suffer a 15 % reduction in
amplification, whereas dry-treated ropes show little effect
of water. The reduction in amplification for wet classic
ropes is due to a combination of water increasing the COF
between the rope surface (mantel) and the Aluminium
belay device while at the same time, water reduces the
distortion energy related to slippage between cords within
the core of the rope. Dry treated, water repellent ropes
show almost no difference in amplification whether wet or
dry.
Appendix 1
Measurements of COF for various ropes
The kinetic COF between the mantel of the rope and pol-
ished Aluminium was measured for rope sliding over a
large radius Aluminium cylindrical bar. The ends of the
rope on either side of the bar were loaded by weights
representing (1) hand force and (2) tension in the rope
connected to the falling climber. For the minimum differ-
ence in weights where the rope slipped freely over the
cylinder, these measurements were used in Eq. (2) to obtain
an estimate of the Coulomb friction coefficient.
Note that the COF between the nylon rope and aluminium
is decreasing with increasing hand force; a result previously
noticed by Titt [1]. For rubber sliding on aluminium, Persson
[14] showed a similar decreasing kinetic COF with
increasing normal pressure; he attributed this to vibrational
energy dissipation excited by the relatively soft polymer
sliding over hard asperities on the aluminium surface. Fenz
[8] measured friction between woven PTFE and stainless
steel which again exhibited a decrease in friction coefficient
with increasing pressure, possibly due to lubrication by
surface melting of the high points on the polymer.
W. J. Stronge, M. Thomas
Appendix 2
Measurement of ‘‘hand force’’
Table 4 lists the mass in kilogram of the maximum weight
lifted by a recreational rock climber using either the left or
right hand gripping a 9.4 mm diameter climbing rope.
These tests were conducted with either a bare hand or the
hand covered by a pigskin belay glove and without wrap-
ping the rope around the hand.
The tests indicate a wide range of hand force (grip
strength) varying from 0.074 to 0.368 kN. With a belay
glove, the hand force is slightly smaller. Generally, these
forces are larger than the 0.16 kN quoted by Manin et al.
[2]. For Table 4 the duration of gripping the rope is\10 s,
similar to the time occurring while holding the initial jolt
Table 2 Kinetic friction measurement for climbing rope sliding over large radius aluminium cylinders (dry state)
Hand
force
(N)
Al. cylinder
radius (mm)
l Edlinger
(new,
10.2 mm)
l Edlinger (used
(1), 10.2 mm)
l Edlinger (used
(2), 10.2 mm)
l Booster Classic
(new, 9.7 mm)
l Booster gold dry
(new, 9.7 mm)
l Ice Line-dry
(new, 8.1 mm)
56 83 0.20, 0.19 0.23, 0.23 0.21, 0.25 0.18 0.19 0.19, 0.20
58 38
96 83 0.19
105 83 0.20, 0.18 0.20, 0.19 0.21, 0.21 0.17, 0.15 0.17, 0.16 0.17, 0.19
154 83 0.17 0.17 0.20, 0.21 0.16 0.17
157 76 0.25
204 83 0.17, 0.16
207 38 0.21
207 76 0.21
207 83 0.20 0.17 0.19, 0.21 0.15 0.16 0.18
253 83 0.19, 0.16 0.17, 0.21 0.15 0.15 0.15, 0.17
351 83 0.18 0.17 0.20 0.15 0.17
401 83 0.17 0.17
499 83 0.17 0.16 0.17, 0.18 0.15 0.14 0.15, 0.15
597 83 0.15 0.16 0.16
794 83 0.15
Table 3 Kinetic friction measurement for climbing rope sliding over
large radius aluminium cylinders (wet state)
Hand
force
(N)
Al.
cylinder
radius
(mm)
lEdlinger
(new,
10.2 mm)
l Edlinger
(used (1),
10.2 mm)
l Edlinger
(used (2),
10.2 mm)
l Ice
Line-dry
(new,
8.1 mm)
56 83 0.23, 0.30 0.27, 0.36 0.23, 0.36 0.23
105 83 0.20, 0.27 0.38 0.22, 0.34 0.20, 0.22
154 83
207 83 0.19, 0.21 0.35 0.18, 0.30 0.19, 0.22
253 83 0.20, 0.21 0.25, 0.26 0.19, 0.26 0.22, 0.22
351 83 0.17, 0.20 0.24, 0.27 0.21, 0.26 0.20, 0.18
499 83 0.17, 0.22 0.25, 0.24 0.24 0.20, 0.21
Table 4 Maximum mass (kg) of weight lifted with one hand using
9.4 mm diameter climbing rope
Bare hand With gloves Max Min
Right Left Right Left
Alan 35.00 35.00 30.00 30.00 35.00 30.00
Margaret 12.50 8.75 12.50 8.75 12.50 8.75
Mary W 18.75 18.75 15.00 12.50 18.75 12.50
Charles 15.00 15.00 15.00 15.00 15.00 15.00
Jim 17.50 22.50 17.50 17.50 22.50 17.50
Mary S 18.75 17.50 15.00 12.50 18.75 12.50
Clare 30.00 25.00 25.00 17.50 30.00 17.50
Dave 37.50 37.50 27.50 27.50 37.50 27.50
Rich 30.00 25.00 30.00 25.00 30.00 25.00
Carrie 22.50 22.50 22.50 20.00 22.50 20.00
Oliver 25.00 25.00 15.00 17.50 25.00 15.00
Rob 17.50 17.50 17.50 17.50 17.50 17.50
Dan 15.00 15.00 15.00 15.00 15.00 15.00
Bill 7.50 12.50 7.50 15.00 15.00 7.50
Virgil 25.00 25.00 25.00 25.00 25.00 25.00
Mass (kg) Weight (kN)
Max. 37.50 0.368
Min. 7.50 0.074
Average 20.27 0.199
Effectiveness of mountaineering manual belay/abseil devices
during a climbers fall [11]. The grip strength decreases
with increasing time after this initial period [15].
Additional tests on just 2 recreational climbers measured
the influence on hand force (grip strength) of rope diameter
and whether the rope was wet or dry. The tests were con-
ducted on an Apollo 11 mm, Booster Dry 9.7 mm and Ice
Line Dry 8.1 mm ropes; either dry or after soaking in water
for 12 h. The results indicated that there was no significant
influence resulting from whether the rope was dry or wet.
There was however, a significant reduction in hand force
for the smaller diameter ropes. For the 8.1 mm Ice Line the
hand force was 70 % of that for the 9.7 mm Booster rope.
No significant difference in grip strength occurred between
the 11 mm Apollo and the 9.7 mm Booster ropes
(Table 5).
References
1. Titt J (2009) Belay device theory, testing and practice. http://
www.bolt-products.com/Glue-inBoltDesign.html
2. Manin L, Richard M, Brabant J-D, Bissuel M (2006) Rock
climbing belay device analysis, experiments and modelling. In:
Moritz EF, Haake S (eds) Engineering of sport 6. Springer,
Berlin, pp 69–74
3. Beverly M, Attaway S (2005) Hang em’ high: how far can you
trust your belay device. Int’l Technical Rescue Symposium
4. Pavier M (1998) Experimental and theoretical simulations of
climbing falls. Sports Eng 1:79–91
5. Attaway S (1996) Rope system analysis. http://lamountaineers.
org/xRopes.pdf
6. Jung JH, Pan N, Kang TJ (2008) Generalized capstan problem:
bending rigidity, nonlinear friction and extensibility effect. Tribol
Int 41:524–534
7. Belofsky H (1976) On the theory of power transmission by
V-belts. Wear 39:263–275
8. Fenz D (2002) Frictional properties of non-metallic materials for
use in sliding bearings: experiments. http://mceer.buffalo.edu/
publications/reesaccom/02-SP09/pdfs_screen/19_Fenz.pdf
9. Fuss FK, Niegl G (2010) Understanding the mechanics of
dynamic rope brakes. Procedia Eng 2:3323–3328
10. Nikonov A, Saprunov B, Zupancic B, Emri I (2011) Influence of
moisture on functional properties of climbing ropes. Int J Impact
Eng 38:900–909
11. Spierings AB, Henkel O, Schmid M (2007) Water absorption and
the effect of moisture on the dynamic properties of synthetic
mountaineering ropes. Int J Impact Eng 34(2):205–215
12. Song J, Ehrenstein GW (1990) Effect of water uptake on the
properties of polyamides. Kunstst Ger Plast 80(6):722–726
13. Cotugno S, Mensitueru G, Musto P, Nicholais L (2010) Water
sorption and transport in polymers. In: Nylon and ropes for
mountaineering and caving Turin: Italian Alpine Club Technical
Committee, 8 March 2002; CCMT Centro Studi Materiali e
Tecniche
14. Persson BNJ (2001) Theory of rubber friction and contact
mechanics. J Chem Phys 115(8):3840
15. Nakada M, Demura S, Yamaji S, Nagasawa Y (2005) Exami-
nation of reproducibility of grip force and muscle oxygenation
kinetics on maximal repeated rhythmic grip exertion. J Physiol
Anthropol Appl Human Sci 24(1):1–6
Table 5 Weight (kN) lifted with one hand using dry and wet ropes
without glove
Rope (diameter) Dry Wet
Bill (kN) Mat (kN) Bill (kN) Mat (kN)
Apollo (11 mm) 0.157 0.206 0.186 0.226
Booster (9.7 mm) 0.157 0.206 0.157 0.177
Ice Line (8.1 mm) 0.108 0.157 0.108 0.157
W. J. Stronge, M. Thomas
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